Question: $\dfrac{ -4q - 9r }{ -10 } = \dfrac{ 5q - s }{ -2 }$ Solve for $q$.
Solution: Multiply both sides by the left denominator. $\dfrac{ -4q - 9r }{ -{10} } = \dfrac{ 5q - s }{ -2 }$ $-{10} \cdot \dfrac{ -4q - 9r }{ -{10} } = -{10} \cdot \dfrac{ 5q - s }{ -2 }$ $-4q - 9r = -{10} \cdot \dfrac { 5q - s }{ -2 }$ Reduce the right side. $-4q - 9r = -{10} \cdot \dfrac{ 5q - s }{ -{2} }$ $-4q - 9r = {5} \cdot \left( 5q - s \right)$ Distribute the right side $-4q - 9r = {5} \cdot \left( {5q} - {s} \right)$ $-4q - 9r = {25}q - {5}s$ Combine $q$ terms on the left. $-{4q} - 9r = {25q} - 5s$ $-{29q} - 9r = -5s$ Move the $r$ term to the right. $-29q - {9r} = -5s$ $-29q = -5s + {9r}$ Isolate $q$ by dividing both sides by its coefficient. $-{29}q = -5s + 9r$ $q = \dfrac{ -5s + 9r }{ -{29} }$ Swap signs so the denominator isn't negative. $q = \dfrac{ {5}s - {9}r }{ {29} }$